An expansion move that preserves complete foldability

An expansion move that preserves the tricolorability (complete foldability) of  a triangulation.

Like the Pachner moves in the previous post, the composite move that preserves the tricolorability or tripartite-ness of a triangulation has a dual version that acts  on the trivalent connectivity map.

The expansion move acts on the dual connectivity map (dashed lines) in a predictable way.

Expansion in the connectivity map is simply the insertion of a digon in an edge. This increases face count by one, vertex count by 2, edge count by 3.

Expansion in the connectivity map is simply the insertion of a digon in an edge.

Moves that preserve the tricolorability of the triangulation preserve the local bipartite-ness of the connectivity map.